The Wearever Carpet Company manufactures two brands of carpets-shag and sculptured-in 100 yard lots. It requires...

The Wearever Carpet Company manufactures two brands of carpets-shag and sculptured-in 100 yard lots. It requires 8 hours to produce one lot o shag carpet and 6 hours to produce one lot of sculpture carpet. The company has the following production goals, in prioritized order:

1) Do Not underutilize production capacity, which is 480 hours.

2) Achieve product demand for shag is more important than meeting demand for sculptured, by a ration of 5 to 2.

3) Limit production overtime to 20 hours

Solve:

a) Fromulate a Goal Programming Model to determine teh amount of shag and sculptured carpet to produce the best meet the company's goals.

b) Solve his model by using the computer (Excel and Solver)

Please help solve this. Use Excel to set up the table and utilize solver. I need help with that part and explaining. Thank you.

Solutions

Expert Solution

(a)

Let X1 and X2 be the number of lots of shag and sculpture carpets to be produced respectively. Also, Let Ui and Oi be the under and overachievements of the i-th goal.

Objective function: Minimize Z = 3*U1 + 2*(5/7)*U2 + 2*(2/7)*U3 + 1*O1
Subject to,
8X1 + 6X2 + U1 - O1 = 480 (min labor hours - goal 1)
X1 + U2 - O2 = 40 (demand for X1 - goal 2)
X2 + U3 - O3 = 50 (demand for X2 - goal 2)
8X1 + 6X2 + U1 - O1 = 480 (max labor hours - goal 3)
X1, X2, Ui, Oi >= 0

----------------------------

(b)

keosha answered 1 year ago

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